What Are Your Chances?

by Laurie Townsend

What are your Chances? is about how to determine the probability of events that are used in playing common games. My unit is probability and games are a very relevant application of probability. I used clip art from Microsoft and I drew some of the pictures. Using games adds interest to the subject. Most students will have played some sort of board or card games. If they haven’t it is something that they can try for themselves very easily. This could be used as a pre reading strategy or used as a review of basic concepts.

What Are Your Chances?


Systems of Linear Equations: Solving Methods

By: Erin Weld

A system of Linear Equations is a fundamental concept that follows the development of understanding equations. The idea of linear is that these equations are easiest to understand for they are a straight line and have a constant change. A system of linear equations is a set of equations that can be dealt with together, and the resulting answer is a solution set that graphs to a unique point, no point, or multiple different points. A system of linear equations can be solved by one of three different methods: elimination, substitution, and graphically.

This book walks students through each method of solving a system of linear equations. The book uses the same system of equations for each method, which shows that each method produces the correct solution set for the system. The book also addresses the idea of double checking your work, which is an imperative concept for mathematics.

Using this digital text in your classroom can provide an additional source for information and therefore we can use some of the literacy techniques with this. You can have students complete a graphic organizer; sequencing would be very applicable for this particular reading. You could have student complete a KWHL prior to reading, which will allow them to make connections between equations and what the implications for the interaction between multiple questions. Finally you can have a student create a digital text reading a topic, which would be considered a post reading strategy. Obviously we can see that this digital text concept can be used as a pre-reading, during reading and finally a post-reading strategy to help incorporate the new common core standards into a classroom.

Solving Systems of Linear Equations


Conic Sections: A Summary

By Justin Ingerick

Conic Sections are four fundamental graphs used in high school level mathematics. Where do they come from? What are the most important aspects of them? How are they constructed? All of these questions (and more) can be explored through this digital text! Short enough to remain attentive, but dense enough to enforce vocabulary and highlight relationships, this text is a very useful tool for any student in trigonometry.

This book can be beneficial to both students and teachers through classroom discussions. During the unit on conic sections, the teacher can use this book to focus the students on the important aspects of conic sections. Students will be able to visually see the differences in the conic sections as well as learn where they come from (the intersection of a plane and a right circular cone). Reading and interpreting the equations and variables in this book is also a skill that students will work towards enhancing through strategies such as think-alouds or "It says, I say, so then." Overall, this digital text highlights the connections among computational algebra, geometric constructions, and trigonometric ideas.

Although this book is useful for recapping or recalling information, it should be supplemented with hands on activities that coincide with the major components depicted in the book. Before the conclusion of the book, the teacher can pose a question to the students about where conic sections can be found in the real world. Students will enjoy this brainstorming exercise as well as learn how to connect mathematics to real world problems as the teacher displays the final page in the book, which identifies conic sections in the real world. Finally, students are able to feel less intimidated by conic sections because this book will guide them through the important aspects and allow them to reach their learning potential.


To research more stuff about Freedom Mentor then visit Freedom Mentor.Student Created Books

An Acrostic Look at Squares
By Jeremy Willard
I would recommend using this book as either a pre-reading tool or a post-reading tool. This would be a great way to introduce students to squares before they read a section in their textbooks for example. This book goes through and describes different characteristics of a square which could be useful to show students and give them some information before they start reading. This could also be a post-reading strategy by a review of the material that was read. It could be used as a way to see if students understand and remembered the characteristics of a square.

http://www.tikatok.com/uploads/pdfbook/hires/an-acrostic-look4feef004e378a2_04989093.pdf

Taking a Walk Around the Unit Circle

by Jodi Iman

I would use this book as a pre-unit tool. I think it is a good way to extract prior knowledge of the subject. The idea for this book is for students taking pre-calc or algebra 2, where they would have some experience with the unit circle and basic trig in previous years. This is a good refresher for students restarting the unit.
I think good literacy strategies to connect with this book would be an anticipation guide, to see what the kids remember before they read the book. Another good strategy would be a KWL. This would be a good sequence for students, begin with what they know as a discussion or brainstorm in class. Then show the book and have them discuss what they still want to know after reading, and after the unit have them recap and discuss what they learned.


The Parallelogram Who Couldn't Find His Was Home.
By: Max Zeller
Summary: Perry is lost and wants to find his way home. On his adventue he runs into different types of quads and talks to them about how they have different charecteristics.

I recommend this as a post reading strategy where the students become comfrotable with the vocabulary and then have them create their own. I would use mine as an exemplar.

Natural Nick's Search for Truth

By: Mike Burke

Summary: Natural Nick doesn't know much about his family, and he wants to! Learn about Nick's family in this short story about the classification of numbers, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers!

I recommend a pre-reading strategy of having students take their own family members and classify them into some sort of hierarchy. This will engage their knowledge of classification and also get them in the mind set of family trees.


The Mysterious Case of Scarlet Scalene

By: Jessica Vito

Summary: In the following story, a young acute triangle is accused of a crime he did not commit, because of a misapplication of triangle congruences that many geometry students make.
The story illustrates why the side, side, angle postulate does not hold true and uses it to prove the innocence of the defendant. After reading this story a recommended pos t- reading strategy would be
to create a graphic organizer determining which triangle postulates do show congruence and which of those do not.

The Land of Circles

By Matthew Marion


Videos

Trigonometric Ratios

Poem/Song

Table of Contents

We Will Graph You!

By: Carter, J. Retrieved on June 2, 2010 from www.rogertaylor.com/clientuploads/documents/references/Mathsongsing-a-long.pdf
Posted by: Donna

We Will Graph You (Tune: “We will Rock You”)
Buddy, you’re a man with a hard time graphing.
All you need to do is find the m and the b
It’s not too hard you see,
You put your pencil on the b.
Graphing’s not as hard as you thought it might be, singing

Chorus: We will, we will graph you!
We will, we will graph you!

Now you’ve got a point on the y intercept.
All you need to do is find the rest of it.
You need the slope to go on,
That’s rise over run.
Delta y in delta x, boy it’s fun, singing….

(Chorus)

Next, take the coefficient of the x baby.
Find two more points and another maybe.
Go up or down first,
Then go across.
I dig graphing lines, I think it’s boss, singing…

(Chorus)

Summary: The song is sung to the tune of We Will Rock You by Queen and indicates the necessary steps to take when graphing a line using the slope intercept form of a line.

Favorite Part: I love that this song is set to a tune that is easily recognized by students, especially during football season. I like that the song describes slope as rise over run, delta y in delta x, the coefficient of x, as well as go up or down first, then across.

Connection to Instruction: Students spend a significant amount of time graphing linear equations. This song is a great way to help students remember to first plot the y intercept then use the slope to plot additional points.

Use of Literary Strategies: This song could be used as a pre-reading strategy to connect with prior knowledge (i.e. remind students how to graph) and as a way to reinforce the vocabulary used in linear equations. Students with musical intelligence may enjoy a new spin on an old but familiar tune.


Quadratic Formula Song

Retrieved on June 4, 2010 from www.youtube.com/watch?v=CnJT1ojHT28
Posted by: Donna
Summary: This video sets the quadratic formula to the tune of Jingle Bells.
Favorite Part: I like that it is clearly done by a group of students and that the result is a fun, catchy tune.
Connection to Instruction: I would use this to encourage students to use mnemonic to help them remember formulas.

Use of Literacy Strategies: This could to be used as a quick pre or post-reading strategy.







Perimeter, Circumference, Area, and Volume

Songs for Teaching Math – Lyrics and Sound Clip
By Kathleen Wiley
Posted by Angela Tessoni
Wiley, K. (2002). Perimeter, circumference, area, volume. Retrieved from http://www.songsforteaching.com/math/geometry/perimetercircumferenceareavolume.php

Perimeter.... It takes the long way 'round.....
Because it measures...... till all the sides are found.....
So take the numbers.... then add them up or down....
And now you've got the perimeter....

RAP:
All around the edge of something if you walk or if you're running...
Just add up the sides you see to get PERIMETER to be.

Circumference..... the distance 'round the earth......
Circumference measures a round object's girth.......
And here's the secret.... there's yet another word....
Circumference is a periphery.

To find circumference..... pi times diameter
Or two times pi, then times the radius
So pick your preference.. but just don't make a fuss..
'Cause both will find the circumference.

RAP:
Now circumference we are doing its a circle for our viewing
We can just go 'round and 'round 'cause never is the end found.

The area..... well, when you measure it....
You just multiply the length times the width
So just remember..... that when you're measuring.....
That length times width equals area.

RAP:
The area is found by multiplying length and width....keep on trying
So now you know it's fun to see what area will always be...

For volume..... it's length...times width...times height...
You just multiply them all to get it right...
When you need volume... well, just don't get uptight...
It's length.... times width.... times height.

RAP:
The volume means what is contained
Inside containers....it's so plain
To see that length times width times height
Is what will make your answer right....

So when you measure make sure you're accurate
'Cause it's important.... to not get in a rut....
Of sloppy habits so just enjoy the
Pure pleasure of math measurements!!



Summary: This is a rap song to help explain the concepts of the measurements of perimeter, circumference, area, and volume. It includes generalized definitions, formulas, and a few applications.
Favorite Part: 3rd rap verse last part: “When you need volume... well, just don't get uptight...It's length.... times width.... times height.”
Connection to Content: Often we just tell our students to memorize these formulas, and we think it is simple, but teenagers have a lot on their mind. Some students may remember the formulas, but could apply them incorrectly. This song is a great way to introduce different types of measurements in a fun way that will be memorable for students. Sometimes just memorizing is not enough, but students love to know the lyrics to songs, so they can sing along!
Literacy Strategy: I would probably use this as a during-reading strategy and have students learn the different parts of the rap throughout the unit. My one modification is that not all the area formulas they have to memorize are here, so maybe a good post-reading assignment may be to assign students to add in their own rap parts for the other formulas. It would be interesting to see how creative the students could get.

Trigonometry

By Tan Pratonix
Posted by Peter Parker
Trigonometry began
When Sine and Cos and Tan
[The latter, a perfect gentleman]
Agreed to work in a Triangle.

Now Sine was cross with Cos
Because she got into a tangle
With Cosec the Smart Alec,
Who had a special angle

For flirty Cotangent
[Also known as Cot]
Whose reputation
[Or shall we say, computation? ]
Was certainly not

Above board, like Tangent
[Also known as Tan,
Who, I repeat, was a perfect gentleman]

Cross-fighting in the Triangle,
They drew an obtuse angle;
And slowly by degrees
Sine began to freeze

Till one fine day,
Cosec ran away
With Cotangent...
Which left a place vacant
For the incorrigible Secant,
Who fought and fell out with Tangent…

In short,
Thanks to Cosec and Cot,
Trigonometry
Had to be abandoned.

Summary: A light humored tale using the vocabulary terms from trigonometry.

Favorite part: The ability of the author to incorporate the actual mathematical relationships into the poem’s story.

Connection to content area: The student can break down the poem to reveal that the relationships in the poem between the characters mirror the actual definitions of the vocabulary as used in trigonometry.

Use of literary strategies: This poem would be good application for the strategy of vocabulary visualization called Key Word. The vocabulary word is written down. Then a picture is drawn to visually show what the term refers to and finally the definition is written to describe what the word means.





Pythagoras

Posted by: Chelsea Griswold
Young, V. (1994). Pythagoras. Retrived September 24, 2009 from www.themathwebsite.com
Summary: This is a short poem about Pythagoras, what he did during his lifetime, and some of his view points on the study of math.
Favorite Quote: “Their teacher said to study, with math, they would go far!”
Connection to content area and literacy strategies:
This is another piece about the history of Pythagoras and his philosophies and relates to the study of the Pythagorean theorem and right triangles. If I were to have students read this I’d as them to do “The Important Thing” summarizer as a post reading strategy. Here students would write a paragraph starting with “The important thing about Pythagoras was….”. The paragraph would then summarize the poem with a few supporting details and a closing sentence. That closing sentence would be in the form “But the important thing about Pythagoras was…”.




The Stanford Statistics Songbook

Posted by: Tyler Spitz

The Stanford Statistics Songbook Matthew Finkelman, Giles Hooker, Armin Schwartzman
http://www.bscb.cornell.edu/~hooker/StanfordStatisticsSongbook.pdf

Help!

Help, I need somebody,
Help, a student, anybody,
Help, I need some help with Stats, help!
When I was doing my experiment today
I never needed any kind of help from my TA
but now the survey is done, and I don't feel so sure
how to find the regression line, significant predictors
Help me if you can, I'm feeling drowned
And I do appreciate your dropin
hours.
Help me get my data figured out,
Won't you please, please help me.
I need your expertise, but I don't want to pay
And my design is flawed in oh so many ways
But I can't find Sequoia, and I don't know what to do
Oh here it is, this must be it: a building called SEQ!
Help me if you can…
Summary: As a Beetles fan, my class might find it humorous if I were try and sing this statistics song to the tune of, “Help”. This could be a great introduction to the start of a statistics unit. Under the link you can find various Beetles tunes related to math.

Favorite: My favorite line has to be the one that reads, “I need your expertise, but I don’t want to pay And my design is flawed in oh so many ways…” Students may be able to not only find humor in stats through this song, but also relate to the idea that apply to statistics.

Connection to content: Although very broad, this song is a good tool for students to start thinking about statistics and the various topics that may be covered during the unit and/or class.

Literacy Strategy: This song could be used when modeling to students how to incorporate music into the mathematics classroom. They would have a chance to showcase their knowledge about a given topic throughout the course via songs.




A Contribution to Statistics

Posted by Jeff Doell

'A Contribution to Statistics' by Wislawa Szymborska From Poems New and Collected (p. 263). Szymborska, Wislawa. (1998). New York: Harcourt. http://www.cs.rice.edu/~ssiyer/minstrels/poems/1267.html

also of interest: "Snapshot of a Crowd" (Szymborska 1998, p 122), which can be connected to random samples and "Possibilities" (214), related to likelihoods and probabilities.

Summary: A poem using statistics to describe the poet's sense of the way the world is.

Connection to Content: Uses the language of statistics to relate certain impressions about the various tendencies of mathematics, though his words are obviously not actually data driven. It would probably miss the point of the poem to ask students were they could look for evidence for Szymborska's claims. But I like it. The following is by me not Szymborska

Favorite Part: Forty Four percent of us are not to be taken lightly, I like those odds.

Reading Strategy: Used as part of a pre-reading activity in which students begin to think about what kind of things can be measured and wihch cannot.

Focusing less
on quantifiable [[#|judgements]],
as if the event or detail
under the microscope
were all there was,
and whether it's typical
or statistically anomalous--
if one in a million
or eight out of ten
[[#|shopping carts]] left unattended
in the early morning sun
are as important as some red wheel barrow--
is of no consequence


The Property Song

Posted by: Bill Heinsler

Song - The Property Song, words by John A. Carter (to the tune of This Old Man)
This property, the Commutative Property,
Tells us that we are free
To change the order of a sum,
Also in a multiplication.

This property, the Associative Property,
Tells us that you and me
Can change the grouping when we multiply,
Do it when you add, it'll make you look sly,

This property, the Identity,
Tells us that so obviously
Anything times one will not change,
Anything add zero will still remain.

This property, the Inverse Property,
Tells us that which we can see
Multiply by the reciprocal to always obtain one,
Add the opposite to anything to always leave none.

This property, the Distributive Property,
Talks to us about a quantity
Which contains a sum and is being multiplied.
Take the product with each term inside.

from the website: http://www.rogertaylor.com/clientuploads/documents/references/Mathsongsing-a-long.pdf (retrieved Oct. 1, 2009)

Favorite Part - Even though this is a corny song, I like that it breaks down all of the major properties that students will encounter as they begin to study algebra. All of these properties play key roles in their understanding and solving of algebraic equations.

Connection to Content - The properties described in the song are fundamental properties of algebraic expressions.

Literacy Strategy - I would use this song to introduce (pre-reading) the reading in the textbook about these properties, or I would use this song during the review (post-reading) after the students have read about the properties from their textbook.



The Transformation Song!

Posted by: Brian Slocum
http://www.youtube.com/watch?v=FGmbvz4fCtw
Summary: A video students made to accompany a song they wrote on transformations.
Favorite Part: It was a creative take on incorporating a transformations project involving a song. I enjoyed having the scrolling words across the screen during the video to follow along with the lyrics. My favorite lyric from the song is

"Reflections are done on a line,
called the mirror line.
The figure is flipped about that line,
and made an opposite."

Connection to Content: Transformations is one unit that really can find a way to incorporate more than just a bunch of numbers. Being creative with projects involving outside sources such as music and poetry can turn a unit a student might not otherwise enjoy into one that they won’t ever forget…but for a good reason.
Literacy Strategy: This makes a great pre-reading strategy as a video to show before assigning students a similar project involving creating their own song or poem on transformations.



Quotes - Statistics

Posted by: Tyler Spitz

Quotes taken directly from
http://www.best-quotes-poems.com/statistics-quotes.html
“Statistics: The only science that enables different experts using the same figures to draw different conclusions.”
Evan Esar, American humorist
“Statistics are like lampposts: they are good to lean on, but they don't shed much light.”
Storm P, Danish writer
“If you want to inspire confidence, give plenty of statistics. It does not matter that they should be accurate, or even intelligible, as long as there is enough of them.”
Lewis Carroll, English author and mathematician
USA Today has come out with a new survey - apparently, three out of every four people make up 75% of the population.
David Letterman

Summary: I love a good quote, sometimes someone has said something in one sentence that would take me a paragraph. To me, quotes are a good way to get the mind thinking about the task ahead.

Favorite: I have two favorite quotes. Lewis Carroll’s explanation sums us statistics well (although they should be accurate) and David letterman’s quote is funny.

Connection to content: When introducing a topic for the first time, or starting on a specific content area once again, it is a good idea to get the students discussing, debating, concluding or just simply talking about the content.

Literacy Strategy: To begin a unit in statistics, I would write down the four quotes on chart paper scattered around the classroom. Students would be in groups of 3-4 and would write down their ideas pertaining to the meaning of the quote. At the end of the activity, groups would complete a jigsaw activity so that all students can see the various interpretations and share their understanding around the new unit.





Circles Radius, Diameter & Pi

Posted by: Andrea Nikolaou
Song retrieved from YouTube Circles Radius Diameter & Pi Math Learning Upgrade

Summary: This song gives students a catchy way to remember what circumference, radius, diameter and area are for a circle.

Favorite part: I like when they describe (pi) as bring 3.14 approximately.

Connections to Content: This works great for 9th graders beginning their unit on circles. It is difficult for students to remember the formula for circumference and area and not mix them up.

Literacy Strategy: The song works as a great way to incorporate the musical/ rhythmic multiple intelligent students.




The Quadratic Formula Song

Posted by: Jason

The Quadratic Formula Song – sung to the tune of “Pop Goes the Weasel”
X equals negative b plus or minus the square root of b squared minus four a c all over 2 a.
S ummary : This song is a catchy way for students to remember the quadratic formula. Sung to the tune of a familiar melody, students walk around humming the song for the rest of the year.
Favorite Part : I like the “all over 2 a” part because that is the part that correlates to the “Pop goes the weasel” in the song and that is my favorite part. Also, it is my favorite because this is often where students mess up the formula because they don’t write the whole numerator over 2a.

Connection to Instruction : This song can be used with a 9th grade algebra class to help students remember a sure-fire way to factor quadratic equations.
Literacy Strategies : Singing the song would likely make the content more memorable for the students. Singing the song could be a pre-reading strategy by introducing the equation.




I Will Derive

Song taken from the Gloria Gaynor song "I will Survive". This may be viewed and heard from
http://youtube.com/watch "
“I Will Derive”
At first I was afraid, what could the answer be?
It said given this position find velocity.
So I tried to work it out, but I knew that I was wrong.
I struggled; I cried, "A problem shouldn't take this long!"
I tried to think, control my nerve.
It's evident that speed's tangential to that time-position curve.
This problem would be mine if I just knew that tangent line.
But what to do? Show me a sign!

So I thought back to Calculus.
Way back to Newton and to Leibniz,
And to problems just like this.
And just like that when I had given up all hope,
I said nope, there's just one way to find that slope.
And so now I, I will derive.
Find the derivative of x position with respect to time.
It's as easy as can be, just have to take dx/dt.
I will derive, I will derive. Hey, hey!

And then I went ahead to the second part.
But as I looked at it I wasn't sure quite how to start.
It was asking for the time at which velocity
Was at a maximum, and I was thinking "Woe is me."
But then I thought, this much I know.
I've gotta find acceleration, set it equal to zero.
Now if I only knew what the function was for a.
I guess I'm gonna have to solve for it someway.

So I thought back to Calculus.
Way back to Newton and to Leibniz,
And to problems just like this.
And just like that when I had given up all hope,
I said nope, there's just one way to find that slope.
And so now I, I will derive.
Find the derivative of velocity with respect to time.
It's as easy as can be, just have to take dv/dt.
I will derive, I will derive.

So I thought back to Calculus.
Way back to Newton and to Leibniz,
And to problems just like this.
And just like that when I had given up all hope,
I said nope, there's just one way to find that slope.
And so now I, I will derive.
Find the derivative of x position with respect to time.
It's as easy as can be, just have to take dx/dt.
I will derive, I will derive, I will derive!

Summary: This song well help students to remember that the definition of a derivative
is the "slope" or line tangent to a curve at a certain point. Specifically in this song the velocity at a point in time.

Favorite Part : "There's just one way to find that slope. And so now I, I will derive" because it reinforces
what the derivative's symbol is and why it is used.

Connection to instruction: Calculus and physics with respect to velocity and time.

Use of Literacy Strategies : Think Aloud while working on a word problem.



The Circle Song

By George Flevares
(sung to the tune of the “Gilligan’s Island” theme)
Creative commons attribution

The Circle is completely round,
no beginning nor end,
with interesting properties
that you will see my friend.

Diameter’s the measure of
the very widest part.
The Radius spokes from center
and it goes half as far.

Circumference is the distance
‘round the outside of the rim.
And then there is the area,
that’s all that’s held within.

There is an amazing number,
the world knows its renown.
We call it by the letter π
and you should right that down.

The number starts out 3-1-4,
its digits never stop,
and if you tried to count them all
your head would surely pop.

Oh well, Cherry π’s delicious,
and Apple π’s r^2 ,
and when it comes to C and A
now you know what to do.


Summary : This song relates π to diameter, circumference, and area. It also provides mnemonics for remembering the formulas for circumference and area.

Favorite Part : The verse that reinforces the idea that π never terminates is my favorite part.

Connection to Instruction : This song can be used with math classes for grades 6 to 9. The lyrics could bolster the students' understanding of the relationships between the radius and diameter, as well as the radius with area and circumference.

Literacy Strategies : Actively singing the song would likely make the content more memorable for the students. Singing this could be a pre-reading strategy for introducing the vocabulary and relationships before covering the topic. Or, it could be sung post reading as a wrap-up of the topic.





Picture Book

The Number Devil

Enzensberger, H. M. (1997) The Number Devil. New York: Henry Holt and Company, LLC.
Posted by: Donna
Summary: The main character is a young boy named Robert who that hates math and is annoyed the word problems assigned by his boring math teacher, Mr. Bockel. In a dream Robert meets a mischievous Number Devil who explains mathematical principles in unconventional and often bizarre ways.
Favorite Part: I liked the Triangle Numbers on pages 93, 101, and 133-135. The picture made it so much easier to understand the concept.

Connection to Instruction: This book can be used by middle school and algebra teachers to discuss and explore mathematical principles. There are many pictures and diagrams that allow the reader to easily make connections with the mathematical history and principles. Mathematical theory is explored in a way that is fun and creative.


Use of Literacy Strategies: This book can be used by middle school and algebra teachers to discuss and explore mathematical principles. The illustrations in this book are engaging and help the student visualize the math.




Cubes, Cones, Cylinders, and Spheres


Hoban, T. (2000). Cubes, cones, cylinders, and spheres. Greenwillow Books.
Submitted by Angela Tessoni
Summary: This picture book is intended for grade levels: K-2 to help children visualize three-dimensional shapes in the world around them. However, It never hurts to expose teenagers to these shapes as well, especially when they are always looking for connections to real life. This book shows a variety of scenes that include cubes, cones, cylinders, and spheres.
Favorite Part: The castle on the last page of the book. It incorporates the cube, the cylinder, the cone, and the sphere.
Connection to Content: Students area always searching for real-life connections. This is a great book for students to see where these shapes exist in the world around them.
Literacy Strategy: I would use this book to introduce volume and surface area. During the reading of the book, I would have the students identify the shapes and how they are being portrayed or used. A post-reading strategy could be a scavenger hunt for students to go out into their own neighborhoods, or in their home, and try to capture images of three-dimensional solids and classify them with the appropriate names and how they are being used in the real-world (just like the book is doing).




The Story of Mathematics

By: Rooney, Anne. (2008). London: Arcturus Publishing Inc.
Submitted by Peter Parker
Summary: The text contains historical references to the development of mathematical concepts. Included are the histories of: where numbers come from, measurement, geometry (shapes), algebra, infinity, proofs and others. The book gives math more color and depth of interest.

Favorite part: The relevant area to the trigonometry unit is the history of sine, cosine and tangent. The section reveals how sine was identified and calculated over 2000 years ago. Included is an example how the earth’s circumference was calculated around 200 B.C.

Connection to content: This reference connects with many different units. When the historical background and thinking of mathematics is presented, it gives the knowledge and concepts increased importance and relevance.

Use of literary strategies: The passages will complete the math story. KWL can be used by students before, during and after they read the passage. The passages in the book can be used as a handout in the beginning of each applicable unit to activate prior knowledge and give all students additional insights.




What's Your Angle Pythagoras?

Posted by: Chelsea Griswold
Ellis, J. (2004). What’s your angle pythagoras? . Watertown, MA: Charlesbridge.
Summary: This picture book illustrates what Pythagoras might have been like as a boy. It describes how he went to Egypt and learned about right triangles. The book gives a possible scenario of how young Pythagoras might have developed the Pythagorean Theorem.
Favorite Quote: pg 31
“I just had to learn how to look at things from the right angle”
Connection to content area and literacy strategies:
This picture book is all about the Pythagorean theorem and Pythagoras’ history- it directly relates to my unit and my content area. It gives a visual proof of the Pythagorean theorem as well.
Students could use a graphic organizer to record the things Pythagoras learned in Egypt, or an anticipation guide could be used to activate students thoughts on what life might have been like for Pythagoras.



If America Were a Village

Posted by: Tyler Spitz

“If America Were a Village: A Book about the People of the United States” by David Smith

Summary: This book encompasses the world community by incorporating content areas such as geography and global studies and uses interesting statistics, facts and numbers. Students are given an opportunity to gain a better understanding of how statistics play a large part in our everyday lives.
Favorite Part: The sentence that reads, “Only five people in our village of 100 comes from North America”, has to be the most enlightening sentence and may begin to open students eyes to the world around them.

Connection to Content: This book is full of statistics that can easily be used within the statistics unit. For example, we can use the “village of 100” to make hypothesis about the percentages of people in the entire world that speak different languages such as English, French or Spanish (just to name a few).
Literacy Strategy: While reading, students are able to use coding to monitor their thought process. Because there are so many numbers that students will be reading, coding will help keep their thoughts fresh on paper and the data organized. It will also allow students to go back and have a group discussion around which codes they found most interesting.




It's Probably Penny

Posted by Jeff Doell
Leedy, Loreen. (2007). It's Probably Penny. New York: Henry Holt & Co.

Summary - Begining a unit on probability Lisa's teacher gives her an assignment to think of something that will happen, something that might happen, and something that absolutely can't happen. Lisa goes home to her dog and begins her homework. She will walk her dog Penny. Penny will probably bark at a squirrel, she might eat Lisa's peanut butter and jelly sandwich, she proabaly won't become a movie star, and she can't become the President of United States. Lisa Goes on to apply her new found understanding of probability to other events in her life

Connection to content - This book provides a nice way to ease younger students into thinking about probability by creating broud categories to use in considering likelihood.

Favorite Part - I liked the teachers assignment because it helps kids draw a distinction between very unlikely and outright impossible (Leddy 2007, p. 5).

Reading Strategy: I would use this book as an example before assigning a project in which students write a children's book to teach some mathematical concept.




The King's Chessboard

Posted by: Bill Heinsler

The King's Chessboard, by David Birch. Penguin Puffin, 1988

Summary - This story is about a king who wants to thank a man in his kingdom for helping him. The man refuses, but the king insists so they agree that the king will pay the man in grains of rice, doubling every day, for as many days as there are squares on his chessboard. As the days pass, the king realizes just what he agreed to!

Favorite Part - I really like how humbled the king became when he realized just how much rice he would be indebted to the old man (2^63 grains!!!). It is a great example of how fast exponential equations really grow!

Connection to Content - Exponents can be a major hurdle for some students as they [[#|continue]] their studies into algebra. The properties of exponential functions are shown very well in this book, as to just how fast they really do grow.

Literacy Strategy - I would use the think along strategy as I did this reading with my students, having them make predictions and draw on their prior knowledge as we worked our way through the book.



The Quilt Story

Posted by: Brian Slocum

The Quilt Story
In conjunction with Teaching Math With Favorite Picture Books
Johnston, T., & De Paola, T. (1988). The quilt story. New York: Putnam.
Hechtman, J., Ellermeyer, D., & Grove, S.F. (1998). Teaching math with favorite picture books. New York: Scholastic Professional Books.

Summary: This picture book tells the story of a girl named Abigail whose mother makes her a quilt. The girl is very fond of the quilt and takes it with her everywhere she goes. One day her family moves away and feeling saddened that she has left everything else behind, she is comforted by the quilt. One day when she has gotten all the use she can out of the quilt, it is packed away in the attic. Some animals find comfort in the quilt while it is being stored until one day, a different young girl finds the quilt and has her mother stitch it up to be just like new. When this girl’s family moves to a new home and she is saddened, the quilt is again a comforting source for her.

Favorite Part: I loved Tomie dePaola books as a child, and I was very excited to find a book of his I could relate to transformations. The final page of the book displays an image of the quilt, in which one can find various types of symmetries and transformations present.

Connection to Content: I found out about this book through another book, “Teaching Math with Favorite Picture Books” which poses the idea of having students design their own quilt using different types of symmetry and transformations. While this is aimed at younger children, it would also be a great way to work in a sort of “change of pace” assignment for high school students discussing transformations, allowing them to show some creativity, something that Math certainly does not always allow us to do.

Literacy Strategy: Students could engage in doing a group book talk for this activity. After reading through the picture book, each group could give their own presentation, giving explanations to the rest of the class at to how the story could relate to transformations.



G is for Googol

Posted by: Jason
Schwartz, D. M & Moss, M. (1998). G is for Googol . New York: Tricycle Press .
Summary: B is for Binary, F is for Fibonacci, P is for Probability... even a small sample begins to give you the idea that this is a math book unlike any other. Ranging freely from exponents to light-years to numbers found in nature, this smorgasbord of math concepts and trivia makes a perfect classroom companion or gift book for the budding young mathematician at home. Even the most reluctant math student will be drawn in by the author's trademark wit, Marissa Moss's quirky illustrations and funny captions, and the answers revealed in W is for " When are we ever gonna use this stuff , anyway?"
Favorite Part: I love the illustrator’s ( Marissa Moss) quirky illustrations and funny captions, and the answers revealed in W is for "When are we ever gonna use this stuff, anyway?"

Connection to Instruction: The mathematics in this book works for 6 -12. Many mathematical concepts are discussed in very simple language, making it easy for any student to understand.
Use of Literacy Strategies: This book would lend itself nicely to having students journal or write about connections that they can make to other things in the world around them. While it gives examples, students can relate the concepts to things that are more personal.



Sir Cumference and the Dragon of Pi

Posted by: Andrea Nikolaou
Neuschwander, Cindy. Sir Cumference and the Dragon of Pi

Summary:
It is a great story of a heroic young boy, Radius, who must turn his father, Sir Cumference, back into a human. In order to do so, he must figure out the mysterious number (pi) to know how much of the antidote to give his father. He goes around measuring circles all around town. He measures the outside of circles as well as the length of the middle of the circle and divides it to find a similar number among all sizes.

Favorite Part:
When Radius finds out that (pi) must be a little bigger than three by helping his cousin make pies. He found this by cutting dough into strips and making spokes through the middle like a wheel. In doing so he saw that one strip went through the middle of the circled pie and it took three of the same length strips to go around with a little extra space. This space was too small for half a strip or even a fourth, it took about a seventh. That’s when we realized (pi) was about 3 1/7.

Quote: p. 13
The Circles Measure:
Measure the middle and the circle around,
Divide so a number can be found.
Every circle, great and small-
The number is the same for all.
It’s also the dose, se be clever,
Or a dragon he will stay…
Forever.
Connection to Content:
I would use this before going into my unit for the area of circles.

Literacy Strategy:
This book illustrates how no matter what size a circle is, (pi) is the same for each. The part where he is making pie really illustrates how on strip of dough equal to the diameter goes around the circle three times with a little space.
At first it would be read to the class then they would go onto testing their newfound knowledge on their own circles. They may have been asked to bring in a circle from home to test on.
external image Sir%20Cumference%20Dragon%20of%20Pi.jpg




Trade Fiction & Nonfiction

I Hate Mathematics Book

Burns, M. (1975) I Hate Mathematics Book. California: Yolla Bolly Press.
Posted by: Donna
Summary: This book is for students that are convinced that math is no fun at all. The author uses experiments, riddles, and gags to demonstrate that math doesn’t have to be “mad boring”. The book provides an opportunity for students to interact with mathematical concepts in ways that are amusing.
Favorite Part: The chapter named “Maybe Grownups aren’t as Smart as You Think” beginning on page 33. There are numerous experiments, riddles and brain teasers that students can use to test the mathematical savvy of an adult of their choice.
Connection to Instruction: This book can be used in classrooms studying mathematics to show that math is not an impossible subject reserved for only the “smart” kids. I would use this to encourage students to ponder everyday mathematical concepts and to refine their problem solving skills.


Use of Literacy Strategies: There are numerous fun activities and brain teasers that could be used as a pre-reading strategy (warm-up) or post reading strategy (ticket out the door). I would use this book to demonstrate how mathematical concepts can be presented graphically (comic strip fashion).



Kiss My Math

McKellar, D. (2008) Kiss My Math New York: Hudson Street Press.
Posted by: Donna

Summary: This book provides encouragement to middle school girls with math phobia. Kiss My Math takes up where Danica’s first book Math Doesn’t Suck leaves off. She uses real life stories and makes girls feel confident that they can master pre-algebra. There are numerous solved problems where the author clearly explains in conversational English what she is doing.
Favorite Part: What to do if you fail a test on page 59 and the Math Test Survival Guide page 305. Danica reassures readers that it’s not the end of the world if you fail a test. She helps students put a failing grade in perspective and provides advice on how to look at failure as an opportunity to improve. The Math Test Survival Guide provides a practical step by step guide to preparing for an upcoming exam.

Connection to Instruction: This book can be used in classrooms studying pre-algebra, by anyone that has struggled with pre-algebra or by parents or teachers that want a perspective of how middle school girls relate to math. There are many solved problems, diagrams, quotes and sidebars that allow the reader to make connections with the text more easily.
Use of Literacy Strategies: The book provides numerous comparisons and connections that a girl can relate to, each chapter shows notes, examples, practice problems and stories from real girls confessing their math phobias and mathematical triumphs. The author ends each chapter with key take aways that students could use as a model to generate their own key take aways or summaries.



A History of the Circle

Zebrowski, E. (1999). A History of the circle. Rutgers University Press.
Submitted by Angela Tessoni

Summary: This book discusses the history of a circle in technology, culture, history, and science. It also discusses how the circle has contributed to the current knowledge of the world we live in.
A Favorite Part: pg 153 – This section of the book describes how epicenters of earthquakes are found and how the waves that originate from the epicenter are in the form of circular waves.
Connection to Content: Many students ask why something in math is important, and they don’t see the significance in what they are learning. This book would be a great history lesson in terms of mathematics to show students how something as simple as a circle has had such a large impact in our world and in the universe. It is a great resource to show how a circle is applicable. Some of the text could be above the understanding of a high school student, but there is some great material that can be sifted through.
Literacy Strategy: A pre-reading strategy for this book could be a KWL. I could see how much my students already know about a circle, what it is, its characteristics, how it relates to mathematics. Then I could have students read select parts of the book, and I could have them do a think-mark that has them ask clarifying questions, or make connections.




The Complete Idiot’s Guide to Geometry

Szecsi, D. (2007).. New York, Penguin Group.
Submitted by Peter Parker
Summary: The text gives alternate descriptions to the concepts of geometry. The language and writing is in a more reader friendly form than most textbooks.
Favorite Part: The examples used to explain sine, cosine and tangent are very good. The solutions of the examples are very detailed and easily understood. The examples depict applying math to real life problems. On page 232, the example uses sine to find the height of a tree. There are handy vocabulary boxes to highlight definitions.
Connection to content area: The text provides another way of looking at the same trigonometry content. Students may understand concepts more completely when they are exposed to them in an alternate, easy to read form.
Use of literacy strategies: The teacher should be sure to use Access: Textbook Feature Analysis with this book. The text contains valuable highlight boxes and sidebars. The boxes contain vocabulary definitions, important key points (Eureka’s!), boxes with shaded headings for formulas and ones with a horn symbol highlighting a deeper understanding. The students need to be shown that the highlights contain valuable information, information that should not be overlooked.



Journey Through Genius

Posted by Chelsea Griswold
Dunham, W. (1990). Journey through genius. New York: John Wiley & Sons, Inc
Summary: Specifically I’d use pages 48 to 53. These three pages give proof of the Pythagorean theorem and its converse.
Favorite quote: “Note that Euclid’s proposition was not about an algebraic equation…, but about a geometric phenomenon involving literal squares constructed upon the three sides of a right triangle.”
Connection to content area and literacy strategies:
As part of NYS standards students must know how to prove the Pythagorean theorem and its converse. Thus the proofs are the Pythagorean theorem and its converse are directly connected to the content area.
I’d ask my students to use a graphic organizer to clearly delineate the steps of the proof as in the paragraph form found in the book it may be hard to see exactly the steps required.



Freakonomics

Posted by Jeff Doell
Levitt, Steven D., Dubner, Stephen J. (2005). Freakonomics. New York: Harper Collins.

Summary: Using the tools of data analysis and a creative and clever mind, an award winning economist finds statistical evidence for otherwise hidden behavoirs, such as cheating and discrimination, utilyzing unusual data sets left by self intersted behavior that most of us would never see to construct arguments that must be taken seriously.

Connection to Content: While certain chapters, one investigating the business-like operation of a crack gang and another revealing a link between abortion and street crime, may be inappropriate for students, the book is accessible to high school students, and may get the interested and excited about well reasoned and data driven arguments

Favorite Part: "He also believes employees further up the coorporate ladder cheat more then those down below. . . Feldman wondered if the executives cheated out an over developed sense of entitlement. What he didn't consider is that perhaps cheating was how they got to be executives." (Levitt & Dubner 2005 p. 50)

Pre-Reading Strategy: I would use a jigsaw method, giving different chapters to different groups of students and having them explain the teext to each other in their base groups.




Crimes and Mathdemeanors

Posted by: Bill Heinsler

Crimes and Mathdemeanors, by Leith Hathout. AK Peters Ltd. 2007

Summary - This book is a collection of stories about a boy named Ravi that helps the local police chief solve mysteries using his genious brain and his amazing mathematical knowledge. All of the stories are around 10 pages, and the solutions are separate, so you have time to think before you read them.

Favorite Part - I discovered this book at Barnes and Noble, and it reminds me so much of the Encyclopedia Brown books that I loved as a kid! With all of the stories being short, it would be very easy to implement these into the classroom.

Connection to Content - While there is not a lot of algebra in this book, the math in the book is spot on and readers that really want to figure out the solution to any of the crimes described in the book could do so without any advanced degrees, but you do need to think outside the box a little bit, a task which we don't ask our students to do often enough!

Literacy Strategy - I would use think aloud for this book, stopping at key points in the story for the students to really investigate the information that is being presented to them as well as make predictions about "whodunit".



Real-Life Math

Posted by: Tyler Spitz
An excerpt from the book Real-Life Math: Glazer, Evan M. & McConnell, John W. (2002). Real-life Math: Everyday Use of Mathematical Concepts. London: Greenwood Press.

"In medical quality-control testing it is difficult to evaluate the effectiveness of a medical instrument, because many medical measurements such as blood pressure, glucose content in urine, and cholesterol in blood can have a different distribution based on sex or age. Some electronic sensors have the statistics for different population groups in memory. When a reading for a particular type of patient is more than two standard deviations from the mean for his or her group, the instrument will sound a tone, alerting a nurse to a critical value. A dynamic instrument that accounts for patient’s variable establishes a more precise diagnosis of medical problems." (p 129)

Summary: Using real life examples will allow students to make connections to the real world. Another advantage of such an example is to enable the students to better understand the concept.

Favorite: I find this a fascinating fact, one that I didn’t put much thought into or ever realize.

Connection to content: This is a connection to standard deviation. It demonstrates the concept of standard deviation and makes a connection to the math in a real life example.

Literacy strategy: I would use this as a post reading strategy, it may aid students in understanding something they have already read. It can also be used as a pre reading strategy.




The Land of Circles

Posted by: Matthew Marion
Book: The Land of Circles

Connection to Content:
  • The book introduces some key vocabulary and concepts for a geometry unit on circles in a more engaging method than classic textbooks. Vocabulary used is incorporated from material incorporated in a New York State Integrated Geometry classroom. Vocabulary is linked to examples in life, predominately pizza in an effort to help students connect the concept with an easy to remember example. Included are simple diagrams to illustrate and connect the illustrated example with the more abstract concept in mathematics. Minor calculation is included to include the idea that the central angle has the same degree measure as its included arc.

Literacy Strategies:
  • Even though I am attempting to make the vocabulary "user friendly," I believe I would be willing to consider having students use text coding. As students read, they can monitor their understanding of the definitions I have supplied. I would certainly use Five Words/Three Words with my book, I feel this could very actively engage and elicit students to activate prior knowledge. Although the book is very short, I would consider also using think marks.



The Big Book of Mind-Bending Puzzles

Posted by: Cal Dupuis
Stickels, T. (2006). The Big Book of Mind-Bending Puzzles. New York, NY: Sterling Publishing Co., Inc.

Summary: This book is loaded with 644 different math puzzles. They cover all areas of mathematics from logic to spatial/visual puzzles. Ten different categories of math puzzles are presented. One of the areas is probability and there are several such puzzles in the book. Some of them are easy to solve and some are quite challenging. But this depends on the perspective the solver brings to the table. Try your hand at them.

Favorite Part: There were several brainteasing probability puzzles. One of my favorites is the following on page 13:
"Mary has placed two chocolate cupcakes in one drawer of her kitchen. In another drawer, she has placed a chocolate and a vanilla cupcake; and in a third drawer, two vanilla cupcakes. Her brother knows the arrangement of the cupcakes, but does not know which drawers contain each arrangement. Mary opens one of the drawers, pulls out a chocolate cupcake, and says to her brother, "If you can tell me what the chances are that the other cupcake in this drawer is chocolate, I will let you have any cupcake you like." What are the chances that the other cupcake is chocolate?

Connection To Instruction: These puzzles would be great in the door or out the door exercises to formatively assess understanding of probability while teaching the unit. They would also be good material for a substitute teacher to present to the students. Students could work either individually or in groups on the puzzles. It would be best to use them for assessment, but they could be done just for fun as well.

Literacy Strategy: This exercise would definitely appeal to the students with logical-mathematical intelligence traits. A mathematical Think Aloud strategy could be used for this where the problems are broken down into steps to analyze and address the sticking points for the students. Most of the probability problems could be analyzed in the same way.



Conned Again, Watson

Posted by: Andrea Nikolaou
Bruce, Colin. (2001). Conned Again, Watson

Summary:
This novel holds a variety of cases solved by Sherlock Holmes using logic in math. Each chapter holds a new mystery that requires a different concept in math to be solved. It demonstrates common misconceptions and even errors that occur commonly among people. Chapters include such math concepts as the probability of flipping a coin, the birthday paradox, normal distribution/ bell curve, permutations and much more.

Favorite Part: p. 110
This chapter focuses on probability. The men were searching for an unmarked grave and in order to do so they played a game of quizmaster. One piece of chocolate was placed in an empty matchbox while the two remaining boxes remained empty. The boxes were placed on the table and the other man had to pick the box with the chocolate. After his first choice one box was opened to reveal it was empty, after that he was asked if he wanted to choose the other box. He did not. The second box was opened to reveal the chocolate, he was wrong, was it pure luck? The chapter goes on to show how odds can change when you reveal one empty box and you are left with only two boxes.

Quote: Preface
“We all lose time and money every day to bad decisions. Often, we are not even aware of it. We continue in blissful ignorance, happy in the illusion that our native common sense is doing a good job of guiding us.”

Connection to Content:
This book can would for a variety of math topics. It is a great way to show that math is used out of school as well as demonstrating common mistakes people make. This book works best for a high school math class involving probability.

Literacy Strategy:
As a pre-reading strategy I would pick a specific part in the book to read aloud to get them all excited to read on their own.
Students could also keep a journal and make connections to what they have learned in class (during).
Jigsaw groups would also be a great idea for this novel since no chapter connects to the next.

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Bringing Down the House

Posted by Shaun McBride
Mexrich, B. (2003). Bringing Down the House

Summary: A book about the story of six MIT students that used their mathematics knowledge to break Vegas. They played black jack and used their probability and statistics skills to know when to bet and how much to bet. It told the story of their lives while they were doing this.

Favorite Part: “Dad, counters don’t keep track of all the cards. It’s about ratios, good cards to bad.” Pg.96

Connection to Instruction: This would be a book probably more suitable for high school students as some aspects of it may be somewhat inappropriate. It can show the importance that statistics, probability and ratios can have and how real people have used that information.

Use of Literary Strategies: I would use this as a post-reading and have the students decide what the big idea is and give examples of what the players did to be successful.

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A History of Pi

Posted by: George
Beckmann, P. (1993) A History of Pi . New York: Barnes & Noble.

Summary : The author details the historical attempts at finding better approximations for π throughout the ages from the Babylonians to computer age scientists. Although much of the math in the book is beyond the scope of high school geometry course, it is a fascinating read about the universal concept of π. Beckmann's sketches of the various mathematicians give the reader insight into the the culture and attitude toward math of the given times and places he covers.

Favorite Part : p. 61 "Inside the city was the 75-year old thinker who had grasped the secret of the lever, the pulley, and the principle of mechanical advantage. . . . Suddenly a soldier came up to him and bade him to follow Marcellus, but he would not go until he had finished the problem and worked it out to proof. 'Do not touch my circles!' said the thinker to the thug. Thereupon the thug became enraged, drew his sword, and slew the thinker. The name of the thug is forgotten. The name of the thinker was Archimedes."

Connection to Instruction : Select passages from this book can be used in a Geometry class to highlight the significance of π. Also, the short biographical sketches of mathematicians and their accomplishments show how discoveries are often made with the help of predecessors.

Literacy Strategies : Teams of students will be utilizing the multiple intelligences of Interpersonal and Body/Kinesthetic by recreating an ancient Egyptian method for approximating π using twine,pencils, markers, and paper.



A Mathematician Reads the Newspaper

Posted by Randy
Paulos, John Allen. A Mathematician Reads the Newspaper . New York: Basic Books, 1995.
Summary: This book examines the mathematical angles of stories in the news and is structured like a newspaper. The book demonstrates how the media can represent unrealistic numbers to the public that usually go unnoticed because of advertising and the way that the media can stir trouble. Each chapter is a "headline" on everything from politics to fashion and food.

Favorite Part: The author connects how statistics can be when represented by the media and marketing. Each headline is written in an amusing manner and students can relate to the topics.

Connection to Instruction : In terms of mathematics, the author mainly addresses the topics of probability and statistics.

Use of Literacy Strategies: I would use this throughout the year in the areas of probability and statistics, possibly starting in middle school and throughout high school.





Magazines & Newspapers


How Far Away is the Horizon?

Submitted by Peter Parker
http://blogs.discovermagazine.com/badastronomy/2009/01/15/how-far-away-is-the-horizon/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+BadAstronomyBlog+(Bad+Astronomy)
Summary: The article describes how far away the tangent point is when the observer is at different heights off the ground.
Favorite Part: My favorite part is the graphics. The drawings really aid in comprehension. I think that tangents will be easier for the students to understand after reading this article. An interesting part in the article was unrelated to the unit but seems important to mathematics. The author comments on whether the results make sense, the answers must be reasonable, just don’t accept the answer if it came out of the calculator.
Connection to Content Area: This reading will be a good lead in for the unit circle section of the unit. The article will help the students to visualize the components of the unit circle.
Use of Literacy Strategies: The writing is easy to follow and entertaining. The math equations are well explained. The drawing allows the student to grasp how the formula was derived.



The Mathematics Teacher

Retrieved From: http://my.nctm.org/eresources/journal_home.asp?journal_id=2
Submitted by Angela Tessoni

Summary: This journal offers a variety of lesson ideas, activities, etc. for high school teachers. It is a peer reviewed journal so it is not something that you would give your students to necessarily read, possibly only excerpts from the journal depending on the level of understanding from the students, but it is a great resource for a teacher to find great ideas about lessons and activities, and even sample problems that would challenge the students. You must subscribe to journal to get recent copies, but St. John Fisher Colleges has past volumes in the library to photocopy.
A Favorite Part: This was a lesson that involved an investigation into the volume of a pyramid (Albrecht, M. (2001). The Volume of a pyramid: low-tech and high-tech approaches. The Mathematics Teacher, 94(1)) on page 58. It is a first hand account of a math teacher teaching this lesson to her geometry students.
Connection to Content: This journal is a great resource because it gives first had experiences with lessons and activities taught by real teachers from all over the country. Students are always looking to do activities in math that give them a deeper understanding of the concept they are learning and some of these lessons do a great job doing just that.
Literacy Strategies: I could assign a reading from the article that meets the reading level of my students and use a think-aloud to help them work through the text. The activities offered for the articles could be a great post-reading strategy to have them investigate what they have just read about and apply it in some way.





The 2500 Year-old Pythagorean Theorum

Posted by Chelsea Griswold
Veljan, D. (2000). The 2500-year-old pythagorean theorem. Mathematics Magazine, 73(4), 259-272
Summary: This article gives a short history of Pythagoras and his philosophies. Also it provides several different ways of proving the Pythagorean theorem along with the dates when these proofs were developed and who developed them.
Favorite quote: “This (the Pythagorean theorem) is probably the only nontrivial theorem in mathematics that most people know by heart….This ‘Methuselah’ among theorems is one of the most quoted theorems in the history of mathematics…”
Connection to content area and literacy strategies:
This text resource provides five proofs of the Pythagorean theorem as well as a short history for some of these proofs. Proving the Pythagorean theorem is a NYS standard.
For this text resource I would use a think aloud as well as a graphic organizer. The reading level is above that of a ninth grader and the think aloud would help students begin to read the article. Furthermore a graphic organizer would help students to see the connection between the various proofs, the date of their development, and who developed them.



Are NY Juries Adequately Diverse?

Posted by Jeff Doell
Stull, Elizabeth. (2009). Are NY juries adequately diverse? Daily Record
http://findarticles.com/p/articles/mi_qn4180/is_20090917/ai_n35669778/

Summary - Considers the importance of the random sample in the pursuit of justice, and points out that juries in New York are not ethnically representative of the counties in which they are formed. The article also discusses proposed legislation aimed at gathering better data on jury composition.

Favorite Part: I like the fact that this article is both current and local

Pre-reading Activity - Discuss personal experience sitting on a jury of 12 white members that convicted an African American. Is that justice?

Rationale - A recent, local article that articulates the importance of procuring a representative and unbiased sample, as well as the need to collect good data in order to make informed and just decisions.

Student Activity - Investigate source lists for the jury pool in our area, and the American Bar Association's recommended strategies for improving jury pool representativeness.

Connection to Content: Does a jury provide a random sample? Why or why not? How hard is it to create a truly random sample?



Distance Formula

Posted by: Bill Heinsler

Article - "Distance Formula", from the website: http://www.algebra-help.info/distance-formula.php (retrieved Oct. 1, 2009)

Summary - This article gives a great description about the distance formula in mathematics, a key to taking algebraic equations and graphing them on the coordinate plane. It can be the foundation for the bridge between geometry and algebra.

Favorite Part - I really like the way that this article opens, describing that the distance formula is derived from the Pytagorean Theorem. Students will be familiar with this theorem, and it is a great way to show that different branches of mathematics are connected.

Connection to Content - The distance formula is a key formula from geometry that translates graphs into algebraic equations. This formula will come up over and over again throughout high school as well as many of the higher level mathematics at the college level.

Literacy Strategy - I would use the KWL chart after reading this article with my students. It would be an great way to pull out some of their background knowledge before digging too deep into new territory, and also for discovering exactly what the students are interested in learning.



HS Students' Intuitive Understandings of Geometric Transformations

Posted by: Brian Slocum
Hollebrands, K. F. (2004). High School Students' Intuitive Understandings of Geometric Transformations. Mathematics Teacher. 97 (3), 207.
Summary: This article explains a teachers’ process of interviewing each of his 10th grade Geometry students prior to their unit on transformations. This allows him to clear up some misconceptions beforehand and better plan for the activities presented in the unit.
Favorite Part: I liked that the teacher had students work with a collection of points rather than polygons when first working with Geometer’s Sketchpad. As stated in the article, “Students may then realize that the transformation is applied to all points in the plane rather than only to a particular polygon.” (p. 214) This allows for a more natural progression by using simpler units, in this case points, before transforming entire figures such as polygons.
Connections to Content: The article states at the end of the piece that most of the students had more misconceptions in regards to translations as opposed to reflections and rotations. This is contrary to what both the teacher thought ahead of time and I thought prior to reading the article. The article also provides diagrams of what some of these students constructed when asked to show the various types of transformations. This provides valuable input for teachers on how to perhaps better explain or what areas to elaborate more carefully on when teaching the transformations unit.
Literacy Strategy: Time constraints make impossible to interview every student individually before every unit. Instead, future students beginning the transformations unit could read this article They could using the Coding Text strategy to mark up any areas of interest, or to note where a misconception they had coming into the unit was shared with one of the students in the article.



Behold the Miracle of Compounding

Posted by: George
Kiplinger's Personal Finance (2007) Behold the Miracle of Compounding

Summary : Financial literacy is a tool students will need to have throughout their lives. Kiplinger's Personal Finance provides practical advice on topics ranging from banking, investing, and spending. In addition to columns about personal finance, the site also offers calculators and quizzes . The story above talks about the power of compound interest over time and how an early start to investing can be the key to generating high returns in the long run.

Favorite Part : Along with numerous strategies on personal finance, there is a quiz section. Readers can test their knowledge on a wide array of financial topics.

Connection to Instruction : Although this magazine is not specifically geared toward mathematics, the topics of investing, banking, and personal finance lend themselves to discussions of mathematics in everyday life. Topics could include compound interest and rates of return.

Literacy Strategies: Classes could investigate articles using Think-Alouds during reading or narrow in on big ideas post-reading.



Math Skills Not Due to Gender

Postd by: Andrea Nikolaou
Stein, Jeannine (June 2009). Math skill not due to gender, researchers say. Los Angeles Times. Retrived June 1, 2009 from http://www.twincities.com/ci_12499213

Summary:
This article clears the stereotype that math is a male dominated field. It answers three questions that many people consider when discussing the differences between male and female performances in math.

Favorite Part:
But new research from the University of Wisconsin-Madison dispels that myth via a meta-analysis of studies and data showing that the gap is more a cultural than gender-based issue.” So many people feel that woman do not succeed in math therefore not pressuring them to try as hard as their male peers.

Connection to Content:
This article is great for any math class in any year. It is especially important for high school students. Female and male students need to see how far women have come and that they are perfectly capable to get the same grades as their male peers.

Literacy Strategy:
I would use a Think Aloud strategy. This way while it is being read they have to stop and think about it. Have they ever herd any stereotypes against women? Do they feel men are better at math than women? It is important to clear these stereotypes sooner than later.
Students could then continue to find articles throughout the school year that either support or disprove this reading.




Mathematics Magazine

Posted by: Jason
Mathematics Magazine for Grades 1 – 12. Accessed from http://www.mathematicsmagazine.com/#

Summary : This online magazine covers a multitude of topics from any grade level. Also includes problems of the week for viewers to try.

Favorite Part : Credit Card Payment Calculator – Students have very little concept of paying debts and bills. They think that they can just pay the minimum balance. However, this calculator shows the amount of time and how much money would be required to pay off your debts.

Connection to Instruction : I would use the tools under the application menu as teaching aides in class. They show a visual representation of many concepts students struggle with.

Use of Literacy Strategies: Site includes biographies of mathematicians. I could develop an anticipation guide to guide readers through the discovery of some of these great math minds.



101 Uses of a Quadratic Equation

Budd, Chris & Sangwin, Chris (March, 2004). 101 Uses of a quadratic equation. Plus Magazine , 29. Retrieved April 21, 2008 from http://plus.maths.org/issue29/features/quadratic/index-gifd

Summary: Plus magazine is a wonderful source for high school math and has a wealth of information. Each issue contains featured articles on everything from careers in math to reviews on books. This particular article is about the development of the quadratic equation, its history and importance. It is interesting as well as amusing and connects algebra to geometry.

Favorite Part : “But this isn’t what mathematics is about at all. Finding a formula is only the first step on along road. We have to ask, what does the formula mean; what does it tell us about the universe; does having a formula really matter?” because it reminds the reader that math is more than numbers and formulas. Math is connected to other disciplines such as science and social studies.

Connection to instruction: Touches upon how math can be used in agriculture as well as determining the population of rabbits. The article addresses the subjects of area, irrational numbers, the Golden Ratio and more.

Use of Literacy Strategies : This article is probably best for students to read at the end of 9th grade or as a review at the beginning of 10th after being familiar with the quadratic equation. The article is a way of connecting algebra to geometry and the “real-world.”





Other Web Resources


BrainPop

Retrieved from http://www.brainpop.com
Submitted by Angela Tessoni

Summary: This website has plenty of short video clips that explain mathematical concepts in a very simple way. Tim and Moby are cartoon characters (Tim is a man and Moby is a robot) that answer questions sent in from people that are curious about different mathematical concepts. Again a subscription is needed, but you can get a free trial, and some videos you can see without a subscription. Some schools have subscriptions to the website
Two Favorites: http://www.brainpop.com/math/numbersandoperations/pi/ and http://www.brainpop.com/math/geometryandmeasurement/geometry/
These two video clips explain what Pi and Geometry are in very simple ways and doesn’t overcomplicate the definitions.
Connection to Content: This is a great resource to captivate student’s attention to a specific topic. The video clips start out with a question and Tim and Moby do their best to explain it plainly, which is all students are looking for sometimes, something simple, not complicated. There are video clip for many different topics in math, from Algebra to Calculus.
Literacy Strategy: These video clips could be used as a pre-reading strategy. They are simple introductions and do not go into a lot of depth, so it will activate some prior knowledge for a student before the go onto read more in-depth, detailed information about a concept.






Triangles, Circles, and Waves

http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/trig.html
Submitted by Peter Parker
Summary: This is an overview of trigonometry meant to be a review resource. The goal is to refresh a student’s memory of trig facts. The sections of the overview include the basic idea, the trig identities, the unit circle, graphing sine and cosine, and radians.
Favorite quote: “Pretty cool, huh?” The writing in this article has a relaxed air about it. I think this article can help students to have fun learning math.
Connection to content area: The article has a strong connection with the concepts in the sine, cosine, and unit circle unit. This article would be an effective teaching tool at the end of the unit to help hammer home the knowledge and concepts prior to the final unit assessment.
Use of literacy strategies: This article lends itself to the jig saw strategy. There are distinct sections which could be assigned to different student groups. The section reports the students gave to each other would force them to learn the material.





A Pythagorean Theorem and its Many Proofs

Posted by Chelsea Griswold
Bogomolny A., Pythagorean theorem and its many proofs. Interactive Mathematics Miscellany and Puzzles. Retrieved September 24, 2009 http://www.cut-the-knot.org/pythagoras/index.shtml
Summary: This page contains 83 different proofs of the Pythagorean theorem.
Favorite quote: “In algebraic terms, a² + b² = c² where c is the hypotenuse while a and b are the legs of the triangle.”
Connection to content area and literacy strategy:
Proving the Pythagorean theorem is a New York State standard for math.
The literacy strategy I would use here is to ask the students to create a Prezzi presentation comparing and contrasting two of the proofs found on this page.


Statistics: Polls, What the Numbers Tell Us?

Posted by Jeff Doell

Statistics: Polls, what the numbers tell us?, Interactives. retrived October 24, 2009 http://www.learner.org/interactives/statistics/index.html

Description: Follows the polling results of a fictional political campaign considering, sampling, confidence intervals, and sources of error along the way. Has all visitors to the sight take a poll before entering and shares the results, explaining that polled population would not consitute a randsom sample. The sight contains many links to valuable resources including Data and Story Library, Statistics every writer should know, and Gallup.

Connection to Content: Takes students through a virtual campaign showing how pollsters attempt to predict the results and explores the reliability of those predictions, explaining the concepts behind the reliability of statistics along the way, identifying various threats to validity.

Favorite Part: I like the fact that students are required to answer a brief survey before entering the site, creating data students can then view and see how they compare to others who have visited the sight.

Reading Strategy: Pre-reading strategy letting kids use an interactive web-site to explore the predictive capabilities of polling, and how it relates to the concepts of error, random samples and validity.



What is Algebra?

Posted by: Bill Heinsler

Website - http://www.cut-the-knot.org/WhatIs/WhatIsAlgebra.shtml (retrieved Oct, 2, 2009)

Summary - The text on this website provides the reader with some basic background knowledge about where the discipline of algebra came from, and how it has evolved since its creation. The cut-the-knot website in general provides some great interactive activities that teachers and students can use to help foster their edcuation in different mathematical fields.

Favorite Part - I am such a fan of history, and when I found this site I learned a few things myself! I think that as important as it is to look forward to where our understandings are taking us, it is just as important to look back on how we got to the point we are at now. The inclusion of the history of mathematics is going to a part of all of my teaching.

Connection to Content - This text provides some historical references to the origin of algebra, and how it has evolved into what it is today.

Literacy Strategy - I would use the jigsaw strategy with this text, dividing the class to read the two sections of the reading. There are some difficult words in the reading, but I think that the students would be able to handle them, especially when working with each other as they read.


Symmetry

Posted by: Brian Slocum
Website
Symmetry – Student’s Page: Introduction and Definitions
http://www.geom.uiuc.edu/~demo5337/s97a/students.html
Summary: This is a website created by students providing definitions relating to transformations on the home page, and then linking to three sub-pages on reflections, rotations, and translations. Each of these elaborates on the definitions on the main pages in addition to showing some great visuals and activities that supplement them.
Favorite Part: Each of the sections on rotations, reflections, and translations does a great job at being concise but still very informative. The animated image of the butterfly’s wing folding over in the reflections section is a nice touch.
Connection to Content: This is a great resource for visual learners, who perhaps need to see how transformations relate to other aspects of life and not just points or shapes on graph paper.
Literacy Strategy**: Students could do a Jigsaw for this activity, dividing into 3 different groups in order to discuss each of the sections (translations, reflections, and rotations) and then split up into smaller groups of 3 to share their findings with those who read the other sections of the webpage before reporting back to their expert groups what they learned about the other two transformations


Khan Academy

Posted by: Tyler Spitz
http://www.khanacademy.org/

Summary: The website serves as a great, free, easy to access tutor method for students who miss a class, misunderstand a concept, or perhaps need to hear the explanation from another source. The site has various videos that will allow students to understand statistical content areas such as average, variance, standard deviation and much more.

Favorite: How about the entire site! Not only does it have videos on math, but also on other content areas as well.

Connection to content: Students may use this resource on their own time or it can be an instructional tool used by the teacher.

Literacy strategy: I would use the videos as a pre reading strategy, giving the students background knowledge before reading about concepts. It could also be used as a post reading strategy if there is part of a concept that the students may have missed during instructional time.




The Count: Clijsters, Not a Tantrum, Decided Semifinal

Posted by: Cal Dupuis
Bialik, C. (2009, September 16). The Count: Clijsters, Not a Tantrum, Decided Semifinal. Wall Street Journal BLOGS.
Retrieved October 1, 2009, from http://blogs.wsj.com/dailyfix/2009/09/16/the-count-clijsters-not-a-tantrum-decided-semifinal/

Summary: The blog is all about how a Harvard University statistician named Carl Morris performed a probability analysis to show that Serena Williams' famous foot fault and subsequent outburst that cost her match point in the US Open, did not lose her the match, but that Kim Clijsters was likely to win the match before this happened anyway. Assuming the players were evenly matched, Serena had about an 8% chance to win the match before the foot fault occurred.

Favorite Part: Being a tennis player and fan, I always thought Kim had the upper hand in this match anyway. It was a shame that Serena decided to perform her antics and taint Kim's celebration. My favorite part was the actual probability analysis, which is a bit hard to follow, but makes sense to me.

Connection To Instruction: My main objective with using this blog would be to have the students read through it to see if they can understand the probability analysis. It's a real life application of probability. Those interested in tennis should be particularly interested. I would also have a class discussion about whether they agree or disagree with it and why or why not. It could be a controversial topic.

Literacy Strategy: I think the Coding Text strategy would be a good During Reading strategy for this exercise. There are plenty of opportunities to either agree or disagree with it. I'm sure there will be a lot of places where they will not understand it and a few points of That's New or WOW!



Stochasticity

Posted by: Cal Dupuis
News Podcast
WNYC Radiolab. (2009, June 15). Stochasticity. Retrieved September 30, 2009, from http://blogs.wnyc.org/radiolab/2009/06/15/stochasticity/

Summary: This one-hour podcast addresses the subject of stochasticity or randomness of events. The main theme is that strange things really do happen by chance. The narrators discuss several events that seem very unlikely or even miraculous and look at them from a probabilistic vantage point. The podcast also highlights that some events that seem quite improbable are really more probable than one thinks.

Favorite Part: The initial story about Laura Buxton is a real grabber. There was this 10-year old girl named Laura Buxton from England who released a balloon into the air with a message on it to whoever received it to write a letter back to her. The balloon floated 140 miles against the prevailing wind and landed in a hedge near the house of another girl named Laura Buxton who was age 10. Also, the two girls had a lot of things in common. They were not related. A miracle or randomness?

Connection To Instruction: I would have the students listen to the Laura Buxton story. I'd really like them to listen to the whole podcast, since I think it's quite intriguing in relation to probability. But an hour might be too much at a time. Then I would challenge them to explore what they think the probability of the event is. For instance, is Laura Buxton a common name in England? How many Laura Buxtons are there? Do they think this is a random event or is it some kind of miracle? Can miracles really happen?

Literacy Strategy: I think I would try an anticipation guide as a pre-listening strategy. I would introduce such statements as the following for discussion:
1. It is possible for a person to win the NY State Lottery twice in a row.
2. There are a lot of people in the world with the same name you have.
3. It is possible for there to be life on planets in other solar systems in other galaxies.


The Math Forum

Posted by: Andrea Nikolaou
The Math Forum - Ask Dr. Math
Summary: This website has everything from elementary math up to high school and college math. Students can browse through a variety of common questions and answers. Students can even post their own questions.

Favorite part: I love how this site is organized. It makes it very easy to look for any specific question.

Connection to Content: Since this site offers help for any and every grade level it works for any unit. It would be a big help for students to get answers so questions they forget to ask in class or where to shy to ask. It also offers a different explanation to a question they just didn’t understand the answer to in class.

Literacy Strategy: This website gives the Verbal/ Linguistic student the ability to search for their own answers. Reading at their own speed gives certain students to chance to work problems out on their own.





X, Why?

Posted by: George

Burke, C. (2006) (x, why?)

Summary : A NY state math teacher maintains a blog which is primarily composed of comics. He conveys math concepts through amusing, pun-filled comics.

Favorite part : I especially like his Mother's Day comic.

Connection to Instruction : Prior to a unit on transformations, a teacher could use the Mother's Day comic and also The Price of Oil to show rotations about axes.

Literacy Strategies :
You can share the comics with the class and use questions about the images to elicit student responses. For example, with “The Price of Oil,” you could ask, “What is happening to the word OIL?”



Regents Prep

Posted by: Jason
Oswego City School District (2003). www.regentsprep.org .
Summary: This is the website that I find myself using the most as an algebra teacher. This is a fantastic site for any NYS Regents exam that has content that covers all subject areas. It is an interactive website that provides lessons and practice based on specific content area standards.

Favorite Part: They have recently added 3 full-length practice regents exams for algebra. The site also provides in depth explanations and self-check options for students.

Connection to Instruction: Students love being on the computer and now they can not be wasting time sitting in front of the old screen. With students at different levels of need, they can review only those topics that they feel they need to review. That leaves the teacher with more time to do other things in class.

Use of Literacy Strategies: This site’s ability to break down a problem in steps helps the students organize their problems. They also lay out tips for using calculators on different problems. Plenty of diagrams and pictures for those visual learners.





Purple Math

Posted by:George
Stapel, E. (2008) Purple Math

Summary : This website is dedicated to algebra topics and problem-solving techniques.

Favorite Part : The section on translating word problems is my favorite part. This page provides useful guidelines for approaching word problems and key words that should act as clues to the problem solver.

Connection to Instruction : Many students struggle with how to answer word problem questions, and some even give up before trying. The guidelines for word problem decoding could be used at any grade level.

Use of Literacy Strategies : Students could construct a graphic organizer of the webpage. It might look something like this:

Graphic_Organizer_Exemplar.jpg
Graphic_Organizer_Exemplar.jpg